Here are the suitable phrasal verbs filled in for each sentence:

1. The tourists **looked around** the artisan's workshop to see how the handicrafts were made.
2. He decided to **cut down on** fast food and eat more vegetables.
3. We need to go to the store because we've **run out of** milk.
4. The tradition of pottery-making has been **passed down** through generations in our family.
5. She wants to **find out** if there are any good schools in the neighbourhood.
6. She promised to **look after** her elderly neighbour by checking in on her regularly.
7. He **gets on with** his neighbors because he is friendly and helpful.
8. We often **go out** for a walk in the park after dinner.